Assignments• Reading Response for two readings Read the handout Data Analysis and Probability Math Every Secondary… (12.8 -12.9 pp635-650)

Written Response: Which explorations appeal/could you adapt – explain.

also, compare/contrast the two approaches – how would you adapt each to your practice?

• POW due Wed (Abe’s Pennies)

• No articles for today

Article Response due

POW due Wednesday

Math 483

Crossing the riverEight adults and two children need to cross a river. A small boat is available that can hold one adult or up to two children. Everyone can row the boat. How many one-way trips does it take for all of them to cross the river?

Crossing the riverEight adults and two children need to cross a river. A small boat is available that can hold one adult or up to two children. Everyone can row the boat. How many one-way trips does it take for all of them to cross the river?

Can you describe how to work it out for 2 children with any number of adults?

How does your rule work out for 100 adults?

Crossing the riverEight adults and two children need to cross a river. A small boat is available that can hold one adult or up to two children. Everyone can row the boat. How many one-way trips does it take for all of them to cross the river?

What happens to the rule if there are different numbers of children?

Write a rule for finding the number of trips needed for A adults and C children.

Driscoll’s Algebra Habits of Mind

Doing-Undoing: reversibility of processesexample: solve 9x2 – 16 = 0

what equation has solutions and Building Rules to represent Functions:

recognize patterns, organize data with in-out realtionships

Abstracting from Computation:computation freed from the particular numbers

they are tied to in arithmetic

Locker problemThere are 30 lockers in one hallway of Whatcom Middle School. The first student goes down the row and opens every locker. The second student then goes and closes every second locker. Next, the third student goes down the row and changes the state of every third locker (closes if open, opens if closed). Student #4 changes the state of every fourth locker, student #5 every fifth, and so on until 30 students have taken a turn.

Which lockers are open after the 20th student?

Which locker or lockers changed the most?

Locker problem200 lockers and 200 students?x lockers and x students?

• Can I write down a mechanical rule that will do this job once and for all?

• How does the rule work?• Why does the rule work the way it does?• What if I start at the end?

n(x) = number of factors of x

n(6) = 4

n(24) = n(288) = n(23 32 54) =

Classify all numbers n so that n(n) =3

Classify all numbers n so that n(n) =2

Find two numbers n and m so that n(nm) = n(nm) - generalize

Find some n so n(n) =6

IN OUT

+5

x2?

x4

÷8

?x6

-4+2+8

Cutting Through the Layers

Lots of SquaresCan you divide a square into a certain number of smaller squares?

ReversalsTake a three-digit number, reverse its digits, and subtract the smaller from the larger. Reverse the digits of the result and add.

123 -> 321, 321 – 123 = 198198 -> 891, 198 + 891 = 1089

Assignments• Reading Response for two articles will be e-mailed

today• POW due Wed (Abe’s Pennies)• Let me know your teaching schedule @SMS (e-mail

ok)• Your plan for Monday @ SMS if teaching (e-mail ok)